I'm going to echo WHarv here and tell you of my baby. During our first pregnancy with our daughter it was discovered that Mom had gestational diabetes. We were too far into the preganacy to treat it and became parents of a beautiful daughter.
As soon as we found out we were pregnant again daily insulin injections were begun. Upon learning that typically the second child is smaller than the first and insulin always keeps the size of the baby down we were expecting a small baby. As luck would have it we ended up delivering a few weeks early, also.
Our son was born weighing 8 lbs. 13 oz and measured 25 1/2 inches. He was so thin you could actually count his ribs. He was also all arms and legs...so much so, in fact, that the nurses couldn't get the little mittened shirts on him so one kind nurse took some of them, cut the mitts off some and the entire sleeves off others and made shirts with extra long sleeves for him.
We went the first two years worried daily about him. He had terrible breathing problems due to an underdeveloped bronchial tract. I can't begin to count the hospital trips and house calls made by doctors for him when it was too cold to take him to the hospital in his condition.
He literally outgrew the problem and went on to be our version of "Jack Armstrong-All American Boy." He was captain of athletic teams, all conference, class president, etc. He was just graduated by Purdue in May, stands 6'-4 or 6'-5 (he finally grew into those arms and legs) and tips the scales around 230 lbs.
Needless to say, like WHarv's daughter, this child doesn't bear any burden from having a bit of a tough start. I'm sure your grandbaby will be the same way. She'll be in my prayers.